Improved Asymptotic Sphere-Packing Bounds for Subblock-Constrained Codes

Subblock-constrained codes are an important class of constrained codes, having applications in many diverse fields. In this paper, we provide closed-form expressions for the best known upper bounds on the asymptotic rates of subblock-constrained codes for a range of relative distance values via a generalized sphere-packing approach. In particular, we study binary subblock energy-constrained codes (SECCs), characterized by the property that the number of ones in each subblock exceeds a certain thresh-old, and binary constant subblock-composition codes (CSCCs), characterized by the property that the number of ones in each subblock is constant. Improved bounds on the optimal asymptotic rate for SECCs and CSCCs are obtained by applying a generalized sphere-packing approach and judiciously choosing appropriate constrained spaces for estimating asymptotic ball sizes. We also use numerical examples to highlight the improvement.